Cooling of turbine blades in a jet engine is important in order to maintain structural integrity whilst the blades operate at high temperatures approaching if not exceeding the melting point of the materials from which the blades are made. Turbine blades generally include a coolant passage network within their structure within which coolant air circulates in order to cool the blade. Such coolant air must be coupled to the coolant passage network within the blade. Generally, a central coolant supply system is coupled to the blade coolant passage network. Traditionally, a specific connecting hole or passage has been made in the mounting hub or disk to which the turbine blade is secured such that an opening in that blade is substantially aligned with the feed hole or passage in the mounting disk in order to present coolant to the blade coolant passage network. Fabrication of such feed holes in the mounting disk as well as reciprocal holes in the root or connecting end of the blade add significantly to fabrication costs as well as increased mechanical stress levels and their requirement for thicker material. Alternatively, a space can be created between the root end of the blade and the top surface of the mounting disk or hub. This space acts as a distribution gallery for openings connected to a coolant passage network of a blade. These distribution galleries are commonly referred to as a “bucket groove”. Essentially, within the distribution gallery there is a positive pressure differential such that coolant air presented at one end is drawn into the openings for the coolant passage network of the blade. Unfortunately, coolant flow in a distribution gallery is turned sharply at least twice as it passes to the coolant passage network of the blade. Such turning can diminish the pressure differential and so flow rate of coolant air into the blade cooling passage network. Clearly, a reduce flow rate will diminish cooling efficiency and therefore performance.